Stocks closed mixed Wednesday, as bank shares rose and comments by President Barack Obama gave investors hope that a quick deal could be made to avoid the “fiscal cliff.”

“We can probably solve this in about a week, it’s not that tough,” Obama said in lunchtime remarks to the Business Roundtable in Washington. The comments, made just before noon, helped push the market higher.

The Dow Jones industrial average rose 82.71 points to end at 13,034.49. It had been up as much as 137. The Standard and Poor’s 500 closed up 2.23 points to 1,409.28. The Nasdaq composite was down 22.99 points to 2,973.70, held back by a slump in Apple.

Stocks have largely traded sideways for two weeks as investors wait for developments from Washington on crucial budget talks to avoid the “fiscal cliff,” a series of sharp government spending cuts and tax increases scheduled to start Jan. 1 unless an agreement is reached to cut the budget deficit.

Citigroup jumped $2.17, or 6.3 percent, to $36.46 after the bank said it plans to eliminate more than 11,000 jobs, or about 4 percent of its workforce, to cut expenses and improve efficiency.

Apple was among the decliners, falling $37.05, or 6.4 percent, to $538.79. Stifel Financial analyst Aaron Rakers said the drop was in part due to comments from AT&T Mobility chief executive officer Ralph de La Vega, which suggested that smartphone activations this quarter were lagging the same period a year ago.

Stocks are still up on the year, after the Federal Reserve extended its bond-buying program in September, offsetting concern that the European debt crisis was set to spread. The Dow has gained 7 percent and S&P 500 has advanced 12 percent.

A private survey showed Wednesday that U.S. businesses added fewer workers in November, in part because Superstorm Sandy shut down factories, retail stores, and other companies. Payroll processor ADP said employers added 118,000 jobs last month. That’s below October’s total of 157,000, which was revised lower. Investors will also look to the monthly jobs report from the Labor Department Friday for more information about how the economy is doing.

Orders to U.S. factories rose modestly in October, helped by a big gain in demand for equipment that reflects business investment plans. Factory orders edged up 0.8 percent in October, the Commerce Department said Wednesday. That followed a 4.5 percent jump in September.

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